Determine Solutions to Linear Inequalities

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What is a linear inequality?

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A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤). It represents a region of the coordinate plane.

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What does the symbol '≥' mean in a linear inequality?

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'≥' means 'greater than or equal to'. It indicates that the values of the variable can be greater than or equal to a certain number.

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How do you determine if an ordered pair is a solution to a linear inequality?

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To determine if an ordered pair (x, y) is a solution, substitute the x and y values into the inequality. If the inequality holds true, then the pair is a solution.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a shaded region on one side of the boundary line, which is solid if the inequality is '≥' or '≤', and dashed if it is '>' or '<'.

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What does the solution set of a linear inequality represent?

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The solution set represents all the ordered pairs (x, y) that satisfy the inequality, forming a region in the coordinate plane.

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What is the difference between a solid line and a dashed line in the graph of a linear inequality?

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A solid line indicates that points on the line are included in the solution set (for '≥' or '≤'), while a dashed line indicates that points on the line are not included (for '>' or '<').

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Substitute the x and y values of the point into the inequality. If the resulting statement is true, then the point is a solution.

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What is the significance of the y-intercept in a linear inequality?

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The y-intercept is the point where the line crosses the y-axis. It helps in graphing the inequality and understanding the relationship between x and y.

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What does it mean if a point lies outside the shaded region of a linear inequality?

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If a point lies outside the shaded region, it means that the point does not satisfy the inequality and is not part of the solution set.

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